The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points

Details The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points

2006-10-24

arxiv.org/abs/math/0610734v2

Electronic J. of Combinatorics 14(1) (2007), R19

Mathematics

Combinatorics

8 pages, no figures. Minor typos in equations for P_4, AZ_3 in Theorem 3, (38) and (39) corrected thanks to Pierre Lalonde

Scientific paper

We show that the generating function (in n) for the number of walks on the
square lattice with steps (1,1), (1,-1), (2,2) and (2,-2) from (0,0) to (2n,0)
in the region 0 <= y <= w satisfies a very special fifth order nonlinear
recurrence relation in w that implies both its numerator and denominator
satisfy a linear recurrence relation.

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